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anonymous

  • 5 years ago

the parabola has a y-intercept of 5 anf contains the point (2,-3) and (-1,12). what are the coordinates of the vertex?

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  1. amistre64
    • 5 years ago
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    (0,5) (2,-3) (-1,12) right?

  2. anonymous
    • 5 years ago
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    yes

  3. amistre64
    • 5 years ago
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    0a + 0b + 5 = 5 4a +2b + 5 = -3 a -b +5 = 12 ; a = 12-5 +b ---------------------------- a = 7 +b ---------------- 4(7+b) +2b + 5 = -3 28 +4b +2b = -8 6b = -36 b = -6 c = 5 ----------------------- a = 12-5 +b; a = 12-5-6 a = 1 -------------------------- y =x^2 -6x +5 is your equation for hese points

  4. amistre64
    • 5 years ago
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    the vertex is at -b/2a 6/2 = 3 the vertex is at (3,y) y = (3)^2-6(3) +5 y = 9 -18 +5 y = 14 -18 y = -4 vartex is at (3,-4) if I did it right ;)

  5. amistre64
    • 5 years ago
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    you agree or disagree :)

  6. anonymous
    • 5 years ago
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    thanx ..that is the rite answer i agree

  7. amistre64
    • 5 years ago
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    yay!! if you ever wanna know "how" its the right answer... I can do that too :)

  8. anonymous
    • 5 years ago
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    ya..i dont get the first few steps

  9. amistre64
    • 5 years ago
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    we know that these three points are not in a straight line, so that only leaves a parabola as an answer that we can actually get.

  10. amistre64
    • 5 years ago
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    a parabola usually is of the form: ax^2 +bx + c = y ; and you normally try to figure out the "x" and "y" values...but they already give you those right?

  11. anonymous
    • 5 years ago
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    yup

  12. amistre64
    • 5 years ago
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    so we get the first 3 equations: a(0)^2 +b(0) +c = 5 ; (0,5).. c = 5 naturally

  13. amistre64
    • 5 years ago
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    the "variables" we are trying to get them to have on common are the a, b, and c parts so this is almost a backwards solution lol

  14. amistre64
    • 5 years ago
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    a(2)^2 + b(2) + c = -3 4a +2b +5 = -3 4a +2b = -8 right?

  15. anonymous
    • 5 years ago
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    yup..

  16. amistre64
    • 5 years ago
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    a(-1)^2 +b(-1) + c = 12 ; (-1,12) a -b +5 = 12 a - b = 12 - 5 a = 7 +b right?

  17. anonymous
    • 5 years ago
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    oh..i get it!!

  18. amistre64
    • 5 years ago
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    4a +2b = -8 ; so plub if our "value" for "a" 4(7+b) +2b = -8 28 +4b +2b = -8 6b = -36 b = -6 :)

  19. amistre64
    • 5 years ago
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    a = 7+b so... a = 7 -6 = 1 our quad equation becomes: x^2 -6x +5 = y :)

  20. anonymous
    • 5 years ago
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    thanx a lot friend..

  21. amistre64
    • 5 years ago
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    youre welcome :)

  22. anonymous
    • 5 years ago
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    would u like to look through the other question i posted too..

  23. amistre64
    • 5 years ago
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    if I can find it lol

  24. anonymous
    • 5 years ago
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    okay

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